论文信息 - Disjoint homometric sets in graphs

Disjoint homometric sets in graphs

Two subsets of vertices in a graph are called homometric if the multisets of distances determined by them are the same. Let h ( n ) denote the largest number h such that any connected graph of n vertices contains two disjoint homometric subsets of size h . It is shown that ( c log n )/(log log n ) h ( n ) n /4, for n > 3.

János Pach | Michael O. Albertson | Michael E. Young

[1] Sophie Piccard,et al. Sur les ensembles de distances des emsembles de points d'un espace euclidien , 1940, The Mathematical Gazette.

[2] B. Aronov,et al. Discrete and computational geometry : the Goodman-Pollack Festschrift , 2003 .

[3] Gary S. Bloom,et al. A Counterexample to a Theorem of S. Piccard , 1977, J. Comb. Theory, Ser. A.

[4] Steven K. Blau. The Hexachordal Theorem: A Mathematical Look at Interval Relations in Twelve-Tone Composition , 1999 .

[5] G. G. Stokes. "J." , 1890, The New Yale Book of Quotations.

[6] P. Seymour,et al. The Structure of Homometric Sets , 1982 .

[7] Warren D. Smith,et al. Reconstructing Sets From Interpoint Distances , 2003 .

[8] T. Althuis,et al. Graph theoretic aspects of music theory , 2001 .

[9] A. Authier,et al. Diffraction Physics , 1998 .

[10] Peter Gilbert,et al. There Are No New Homometric Golomb Ruler Pairs with 12 Marks or Less , 1994, Exp. Math..

[11] Godfried T. Toussaint,et al. The Continuous Hexachordal Theorem , 2009 .